Theory for diffusive and ballistic air leakage and its application to suction cups

TL;DR

This paper develops a unified theory of air leakage at elastic interfaces, validated with experiments on suction cups, revealing key factors affecting failure time and proposing improved biomimetic designs.

Contribution

The paper introduces a new equation for airflow that bridges diffusive and ballistic limits, applied to suction cups on rough surfaces, with experimental validation and design implications.

Findings

Measured suction cup lifetimes agree with theory for rough surfaces.

Surface roughness below 1 μm causes blockage due to plasticizer diffusion.

Suction cup volume and stiffness significantly affect air leakage and failure time.

Abstract

We have developed a theory of air leakage at interfaces between two elastic solids with application to suction cups in contact with randomly rough surfaces. We present an equation for the airflow in narrow constrictions which interpolate between the diffusive and ballistic (Knudsen) air-flow limits. To test the theory we performed experiments using two different suction cups, made from soft polyvinylchloride (PVC), in contact with sandblasted polymethylmethacrylate (PMMA) plates. We found that the measured time to detatch (lifetime) of suction cups were in good agreement with theory, except for surfaces with the root-mean-square (rms) roughness below $\approx 1 \ {\rm \mu m}$, where diffusion of plasticizer from the PVC to the PMMA surface caused blockage of critical constrictions. Suction cup volume, stiffness and elastic modulus have a huge influence on the air leakage and hence the failure time of the cups. Based on our research we propose an improved biomimetic design of suction cups, that could show improved failure times in varying degree of roughness under dry and wet environments.